Score : $200$ points

Problem Statement

There are $N$ weights called Weight $1$, Weight $2$, $\dots$, Weight $N$. Weight $i$ has a mass of $A_i$. Let us say a positive integer $n$ is a good integer if the following condition is satisfied:

• We can choose at most 3 different weights so that they have a total mass of $n$.

How many positive integers less than or equal to $W$ are good integers?

Constraints

• $1 \leq N \leq 300$
• $1 \leq W \leq 10^6$
• $1 \leq A_i \leq 10^6$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $W$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the answer.

2 10
1 3

3

If we choose only Weight $1$, it has a total mass of $1$, so $1$ is a good integer. If we choose only Weight $2$, it has a total mass of $3$, so $3$ is a good integer. If we choose Weights $1$ and $2$, they have a total mass of $4$, so $4$ is a good integer. No other integer is a good integer. Also, all of $1$, $3$, and $4$ are integers less than or equal to $W$. Therefore, the answer is $3$.

2 1
2 3

0

There are no good integers less than or equal to $W$.

4 12
3 3 3 3

3

There are $3$ good integers: $3, 6$, and $9$. For example, if we choose Weights $1$, $2$, and $3$, they have a total mass of $9$, so $9$ is a good integer. Note that $12$ is not a good integer.

7 251
202 20 5 1 4 2 100

48